I wouldn't count on very good accuracy with the accelerator bullets. I think you are looking at two very different purposes. If you must use one rifle for varmints, paper punching, and big game, how about something like a .308? It's a very accurate cartridge and I've used one for varmints and big game.

The 22.250 is an outstanding varmint and target gun, but as you said it's too light for big game.

The 300 will kick the snot out of you after shooting varmints all day in various field positions. And I've never had any luck with the acclerator bullets, or heard of anyone else having much luck with them.